Pressure,
temperature, density, viscosity and speed of sound variation
for the international standard atmosphere (ISA) can be
calculated for a range of altitudes from sea level upward. This
is done using an exact solution to the hydrostatic equation for
a column of air. The air is assumed to be a perfect gas. In the
lower region, the troposphere, the atmosphere has a lapse rate
(L) of 6.5K/Km. At an altitude of 36089 ft the stratosphere
starts and the temperature remains constant at 217K. The
hydrostatic equation, perfect gas law and the lapse rate
equation are

Solving the hydrostatic equation with a constant lapse rate gives the
resulting pressure variation in the troposphere.

where Po is set at 101.3 kPa.

Solving the hydrostatic equation with a constant temperature gives the
resulting pressure variation in the stratosphere.

where
conditions with subscript (s) are values of altitude (hs),
pressure (Ps) or temperature (Ts) at the tropopause, the start
of the stratosphere, the line dividing the two distinct
atmospheric regions.

Once
pressure has been calculated at a particular altitude, density
is then calculated using the perfect gas law. Viscosity and
kinematic viscosity are found by applying the Sutherland law

And finally speed of sound is found as

where is the Ratio of Specific Heats for air and is equal to 1.4

Based
on the above equations, an
application is available which shows
atmospheric properties for a specific altitude.
This application can
also be used to predict Mach Number, Dynamic Pressure and other
altitude dependent properties if an input speed and reference
length are given.